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Some error properties of segmented hydrologic functions
Author(s) -
Snyder Willard M.
Publication year - 1967
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr003i002p00359
Subject(s) - hydrograph , mathematics , representation (politics) , magnitude (astronomy) , yield (engineering) , function (biology) , chord (peer to peer) , explained sum of squares , computer science , statistics , geography , physics , distributed computing , archaeology , astronomy , evolutionary biology , politics , biology , political science , law , flood myth , thermodynamics
Unknown but mathematically continuous functions can be approximated by connected linear segments. The magnitude of the largest error between segmented and continuous forms is shown to be about ⅔ of the maximum difference between arc and chord of the continuous function. This magnitude decreases rapidly with increasing number of segments. Unknown operational hydrologic functions, such as unit hydrographs or water‐yield recessions, can be derived directly from observational data by the method of least squares, and the solutions for fixed segmented systems can be standardized. The form‐free segmented functions are shown to be capable of better representation of data than incorrectly assumed continuous forms. (Key words: Hydrologic systems; water yield; unit hydrograph)